Unless you inherited your system or something, you definitely set a root password during installation. As sideburns notes, it's mandatory. If you've forgotten the password or for some other reason do not know it, you can try booting your system straight into /bin/bash from the bootloader or using Fedora 22 Live media to boot into rescue mode. Instructions covering both procedures are here.
Try the bash solution first, and if that fails for some reason, try the rescue option. If you can boot into bash directly, you can resolve the issue by simply using the passwd
command as you would from a normal boot, but you won't be prompted for a root password. If you boot into rescue mode, you should be able to chroot
into your old OS (/mnt/sysimage) and use the passwd
command to set your root password.
Of course, you need to figure out why your system will only boot into emergency mode. If you need help with that, you can post another question once you've checked your journal and kernel ring buffer (dmesg) and whatnot for information about your system's problem.
Welcome to ask.fedora. As far as I'm aware, part of installing Fedora is setting the root password; how did you manage to skip this step?